A trust-region method for nonlinear bilevel programming: algorithm and computational experience

Benoit Colson, Patrice Marcotte, Gilles Savard

Research output: Contribution to journalArticle

Abstract

We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, {\it i.e.}, bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments tend to confirm the promising behavior of the method.
Original languageEnglish
Pages (from-to)211-227
Number of pages17
JournalComputational Optimization and Applications
Volume30
Issue number3
Publication statusUnpublished - 2004

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Bilevel Programming
Trust Region Method
Nonlinear programming
Nonlinear Programming
Quadratic Approximation
Experiments
Linear Approximation
Numerical Experiment
Tend
Software
Approximation
Experience

Keywords

  • numerical results
  • Bilevel programming
  • approximation
  • trust-region methods
  • nonlinear programming

Cite this

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abstract = "We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, {\it i.e.}, bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments tend to confirm the promising behavior of the method.",
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A trust-region method for nonlinear bilevel programming: algorithm and computational experience. / Colson, Benoit; Marcotte, Patrice; Savard, Gilles.

In: Computational Optimization and Applications, Vol. 30, No. 3, 2004, p. 211-227.

Research output: Contribution to journalArticle

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AU - Marcotte, Patrice

AU - Savard, Gilles

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AB - We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, {\it i.e.}, bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments tend to confirm the promising behavior of the method.

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KW - Bilevel programming

KW - approximation

KW - trust-region methods

KW - nonlinear programming

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